Exhibit 32(b)

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

    In connection with the Annual Report on Form 10-K of City Holding Company (the “Company”) for the period ending December 31, 2023 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, David L. Bumgarner, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1)the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: February 28, 2024

/s/ David L. Bumgarner

David L. Bumgarner

Executive Vice President, Chief Financial Officer and Principal Accounting Officer